New construction - Is high humidity still normal?

Instead of ventilating repeatedly - just leave the house open. You are not losing any heating energy at the moment.
Certainly, the humidity is somewhat increased at the beginning, and 65% is not problematic as long as you feel comfortable with it. Such days occur in summer. It will settle down. The main thing is that it does not become unpleasantly dry in winter.
This is what it looked like for us last year - the jagged-looking profile moves between 46 and 63 (and that with low-tech heating and without any attention on our part)

Instead of constantly ventilating - just leave the house open. You are not losing any heating energy at the moment. Surely, at the beginning the humidity is somewhat elevated and 65% is not further problematic as long as you also feel comfortable with it. Such days occur in summer. It will settle. The main thing is that it does not become uncomfortably dry in winter. This is how it looked with us last year - the jagged-looking profile moves between 46 and 63 (and that with low-tech heating and without any attention from our side)

I would not generally recommend that. I spent the first year always taking the effort to check how the humidity was outside and then converted it to the current room temperature. Depending on that, I ventilated or not. If it is 26° outside at 65% humidity and 21° inside, you will very quickly have mold if you always keep the window open. Regarding the question from the beginning: This is quite normal for the first year. But if you ventilate wisely, it will settle down over time. In the first year, we still had 1-2 damp spots in a room due to residual moisture in the lowest masonry course. However, with a dehumidifier and regular ventilation, that also disappeared over time. I always recommend installing baseboards only after 1-2 years, so you can react quickly to such things. Don’t be alarmed by heating costs either; they are always higher in the first year than later. The house still dries a lot and requires more energy. As already mentioned, houses were previously left standing to dry first. Nowadays, no one can afford that anymore; the loan has to be paid somehow. So that is completely normal. And do not place furniture directly against exterior walls, but with some distance. That helps the air circulate better. Lastly, it should be mentioned that you moved in during summer. The air is very humid anyway then. The house only really becomes dry in the first winter.

Wait for the first winter. The cold dry air will significantly help to reduce the moisture. Otherwise, everything is normal in a new building, that settles down completely automatically in the second year.